No,
Roles.ApplicationName doesn't indicate which provider is used by roleManager. As I mentioned in my previous post, Roles.ApplicationName is used to fetch roles from aspnet_Roles with specified ApplicationName. You can execute following query in ASPNET database to get an idea how SQL accociates roles with applications:
select RoleName,ApplicationName
from aspnet_roles r join aspnet_Applications a
on r.ApplicationId=a.ApplicationId
That's similar to Membership.ApplicationName.
The future is now...
Sincerely,
LeiJun Jie
Microsoft Online Community Support